A whispering chamber is an elliptically arched chamber. A unique feature of a whispering chamber is that when a person standing at one focus of the ellipse whispers, he can be heard by a person standing at the other focus, regardless of the dimensions of the ellipse from which the dome is built.

Suppose that the dimensions of the ellipse used to create a whispering dome is 200 feet by 380 feet. Walter stands at one focus, and Barbara stands at the other focus.

How far apart are Walter and Barbara?

Enter your answer, rounded to the nearest tenth of a foot.

Guest Jan 15, 2021

#1**+1 **

Assuming that the wider part of the ellipse is horizontal and the center is (0,0)

a = 380/2 = 190

b = 200/2 = 100

So we have this form

x^2/ 190^2 + y^2/100^2 = 1

The focal distance from the center is given by

sqrt [ a^2 - b^2 ] = sqrt [ 190^2 - 100^2 ] = sqrt [26100] = 30sqrt (29)

So....Walter and Barbara are standing 2 * 30sqrt (29) = 60sqrt (29) ≈ 323.1 ft apart

See the graph here : https://www.desmos.com/calculator/62jlku7yf3

CPhill Jan 15, 2021